The load event of the XHR2.upload fires in different times in different implementations.
Firefox fires it too lately (when the download of the response completed and not when the upload actually ends).

iOS/Safari bounce scrolling: If the browser can temporarily scroll above to the top of the page (negative window.pageYOffset || documentElement.scrollTop || body.scrollTop) or below the bottom of the page.

CSS

<select> display in IE6

PNG alpha transparency

The look of the various *-resize cursors is very different across browsers and platforms.

Edge cases

IE CSS bug where certain types of positioning of an <input type=text> element can cause that element's autocomplete box to not render at the same location as the actual input box.

strange treatment of <!-- --> comment nodes in the DOM (in IE)... like in some cases, a comment node will be moved to be a child of the previous element even though it's not a child proper. Can cause things like :empty to fail differently.

resize event firing rate. e.g. you can't keep an element's position smoothly updated in response to resize or scroll.

General undetectables

Testable, but typically not feasible to test just to avoid code forking.

Hardware Acceleration

Whether a CSS transition can use (or did use) accelerated compositing. If an effect isn't going to be hardware-accelerated, then a setTimeout animation is often more performant than a non-accelerated CSS transition. No reliable way to measure the framerate of a CSS transition.

This might not be a complete list

Add to the list if you know more Undetectables. Likewise, link to possible solutions if you think an item listed here can be feature-detected.